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Author's title

Author

*Unverified author*

R Software Module

rwasp_exponentialsmoothing.wasp

Title produced by software

Exponential Smoothing

Date of computation

Mon, 19 Dec 2011 15:20:50 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/19/t1324326169kdorgesdoi4fvtr.htm/, Retrieved Wed, 11 Feb 2026 19:18:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157674, Retrieved Wed, 11 Feb 2026 19:18:35 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W102

Estimated Impact

340

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Exponential Smoothing] [exponential smoot...] [2011-12-19 20:20:50] [76c30f62b7052b57088120e90a652e05] [Current]

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Dataseries X:

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2,2
2,28
2,28
2,28
2,28
2,27
2,28
2,27
2,28
2,28
2,28
2,28
2,27
2,28
2,28
2,28
2,27
2,28
2,27
2,27
2,27
2,27
2,27
2,27
2,27
2,35
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,54
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,66
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93
2,93

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157674&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157674&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157674&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.215389253894429
gamma	FALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.215389253894429 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157674&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.215389253894429[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157674&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157674&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
Parameter	Value
alpha	1
beta	0.215389253894429
gamma	FALSE

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	2.28	2.36	-0.0799999999999996
4	2.28	2.34276885968845	-0.0627688596884455
5	2.28	2.32924912183235	-0.049249121832347
6	2.27	2.31864139022592	-0.0486413902259217
7	2.28	2.29816455747677	-0.0181645574767733
8	2.27	2.30425210699453	-0.0342521069945283
9	2.28	2.28687457122466	-0.00687457122466517
10	2.28	2.29539386245774	-0.0153938624577399
11	2.28	2.29207818990841	-0.0120781899084141
12	2.28	2.28947667759565	-0.00947667759564563
13	2.27	2.28743550307892	-0.0174355030789211
14	2.28	2.27368008307948	0.00631991692052125
15	2.28	2.28504132526966	-0.00504132526966439
16	2.28	2.28395547798119	-0.00395547798119233
17	2.27	2.28310351053003	-0.0131035105300272
18	2.28	2.27028115517357	0.0097188448264327
19	2.27	2.28237448990945	-0.012374489909448
20	2.27	2.26970915776053	0.000290842239472067
21	2.27	2.26977180205349	0.000228197946511077
22	2.27	2.26982095343893	0.000179046561072038
23	2.27	2.26985951814413	0.000140481855870345
24	2.27	2.26988977642625	0.00011022357374868
25	2.27	2.26991351739956	8.64826004374208e-05
26	2.35	2.26993214482235	0.0800678551776546
27	2.54	2.36717790040999	0.172822099590012
28	2.54	2.59440192349715	-0.0544019234971493
29	2.54	2.58268433378468	-0.0426843337846763
30	2.54	2.57349058697781	-0.0334905869778144
31	2.54	2.56627707443618	-0.0262770744361762
32	2.54	2.56061727497884	-0.0206172749788398
33	2.54	2.55617653550381	-0.0161765355038113
34	2.54	2.55269228359105	-0.0126922835910488
35	2.54	2.54995850209816	-0.00995850209815607
36	2.54	2.54781354776133	-0.00781354776132837
37	2.54	2.54613059353875	-0.00613059353874723
38	2.54	2.54481012957051	-0.00481012957050631
39	2.54	2.54377407935118	-0.00377407935117935
40	2.54	2.54296118321559	-0.00296118321559069
41	2.54	2.54232337617214	-0.00232337617213974
42	2.54	2.54182294591191	-0.00182294591190635
43	2.54	2.54143030295205	-0.00143030295205104
44	2.54	2.54112223106637	-0.00112223106636566
45	2.54	2.54088051455428	-0.000880514554284062
46	2.54	2.54069086118139	-0.000690861181393831
47	2.54	2.54054205710699	-0.000542057106988736
48	2.54	2.54042530383115	-0.000425303831146362
49	2.54	2.54033369795628	-0.000333697956277135
50	2.66	2.54026182300245	0.119738176997552
51	2.66	2.68605213960863	-0.0260521396086304
52	2.66	2.68044078869597	-0.0204407886959741
53	2.66	2.67603806246973	-0.0160380624697343
54	2.66	2.67258363616047	-0.0125836361604659
55	2.66	2.66987325615658	-0.00987325615658419
56	2.66	2.66774666287951	-0.00774666287950909
57	2.66	2.66607811494172	-0.00607811494171973
58	2.66	2.66476895429934	-0.0047689542993381
59	2.66	2.66374177279095	-0.00374177279094701
60	2.66	2.66293583514126	-0.00293583514126272
61	2.66	2.66230348780063	-0.00230348780062917
62	2.66	2.6618073412819	-0.00180734128189641
63	2.66	2.66141805939166	-0.00141805939165618
64	2.66	2.66111262463731	-0.00111262463730943
65	2.66	2.66087297724681	-0.000872977246814788
66	2.66	2.66068494732896	-0.000684947328956742
67	2.66	2.66053741703482	-0.000537417034815579
68	2.66	2.66042166318066	-0.000421663180656395
69	2.66	2.66033084146278	-0.000330841462780285
70	2.66	2.66025958176695	-0.000259581766954398
71	2.66	2.66020367064385	-0.000203670643845744
72	2.66	2.66015980217583	-0.000159802175827561
73	2.66	2.66012538250441	-0.000125382504405191
74	2.93	2.66009837646033	0.26990162353967
75	2.93	2.98823228577943	-0.0582322857794346
76	2.93	2.97568967719284	-0.045689677192835
77	2.93	2.96584861171159	-0.035848611711593
78	2.93	2.95812720598188	-0.0281272059818818
79	2.93	2.95206890807131	-0.0220689080713092
80	2.93	2.94731550242757	-0.0173155024275653
81	2.93	2.94358592927889	-0.0135859292788849
82	2.93	2.94065966610804	-0.0106596661080434
83	2.93	2.93836368857827	-0.0083636885782683
84	2.93	2.93656223993559	-0.0065622399355898

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2.28 & 2.36 & -0.0799999999999996 \tabularnewline
4 & 2.28 & 2.34276885968845 & -0.0627688596884455 \tabularnewline
5 & 2.28 & 2.32924912183235 & -0.049249121832347 \tabularnewline
6 & 2.27 & 2.31864139022592 & -0.0486413902259217 \tabularnewline
7 & 2.28 & 2.29816455747677 & -0.0181645574767733 \tabularnewline
8 & 2.27 & 2.30425210699453 & -0.0342521069945283 \tabularnewline
9 & 2.28 & 2.28687457122466 & -0.00687457122466517 \tabularnewline
10 & 2.28 & 2.29539386245774 & -0.0153938624577399 \tabularnewline
11 & 2.28 & 2.29207818990841 & -0.0120781899084141 \tabularnewline
12 & 2.28 & 2.28947667759565 & -0.00947667759564563 \tabularnewline
13 & 2.27 & 2.28743550307892 & -0.0174355030789211 \tabularnewline
14 & 2.28 & 2.27368008307948 & 0.00631991692052125 \tabularnewline
15 & 2.28 & 2.28504132526966 & -0.00504132526966439 \tabularnewline
16 & 2.28 & 2.28395547798119 & -0.00395547798119233 \tabularnewline
17 & 2.27 & 2.28310351053003 & -0.0131035105300272 \tabularnewline
18 & 2.28 & 2.27028115517357 & 0.0097188448264327 \tabularnewline
19 & 2.27 & 2.28237448990945 & -0.012374489909448 \tabularnewline
20 & 2.27 & 2.26970915776053 & 0.000290842239472067 \tabularnewline
21 & 2.27 & 2.26977180205349 & 0.000228197946511077 \tabularnewline
22 & 2.27 & 2.26982095343893 & 0.000179046561072038 \tabularnewline
23 & 2.27 & 2.26985951814413 & 0.000140481855870345 \tabularnewline
24 & 2.27 & 2.26988977642625 & 0.00011022357374868 \tabularnewline
25 & 2.27 & 2.26991351739956 & 8.64826004374208e-05 \tabularnewline
26 & 2.35 & 2.26993214482235 & 0.0800678551776546 \tabularnewline
27 & 2.54 & 2.36717790040999 & 0.172822099590012 \tabularnewline
28 & 2.54 & 2.59440192349715 & -0.0544019234971493 \tabularnewline
29 & 2.54 & 2.58268433378468 & -0.0426843337846763 \tabularnewline
30 & 2.54 & 2.57349058697781 & -0.0334905869778144 \tabularnewline
31 & 2.54 & 2.56627707443618 & -0.0262770744361762 \tabularnewline
32 & 2.54 & 2.56061727497884 & -0.0206172749788398 \tabularnewline
33 & 2.54 & 2.55617653550381 & -0.0161765355038113 \tabularnewline
34 & 2.54 & 2.55269228359105 & -0.0126922835910488 \tabularnewline
35 & 2.54 & 2.54995850209816 & -0.00995850209815607 \tabularnewline
36 & 2.54 & 2.54781354776133 & -0.00781354776132837 \tabularnewline
37 & 2.54 & 2.54613059353875 & -0.00613059353874723 \tabularnewline
38 & 2.54 & 2.54481012957051 & -0.00481012957050631 \tabularnewline
39 & 2.54 & 2.54377407935118 & -0.00377407935117935 \tabularnewline
40 & 2.54 & 2.54296118321559 & -0.00296118321559069 \tabularnewline
41 & 2.54 & 2.54232337617214 & -0.00232337617213974 \tabularnewline
42 & 2.54 & 2.54182294591191 & -0.00182294591190635 \tabularnewline
43 & 2.54 & 2.54143030295205 & -0.00143030295205104 \tabularnewline
44 & 2.54 & 2.54112223106637 & -0.00112223106636566 \tabularnewline
45 & 2.54 & 2.54088051455428 & -0.000880514554284062 \tabularnewline
46 & 2.54 & 2.54069086118139 & -0.000690861181393831 \tabularnewline
47 & 2.54 & 2.54054205710699 & -0.000542057106988736 \tabularnewline
48 & 2.54 & 2.54042530383115 & -0.000425303831146362 \tabularnewline
49 & 2.54 & 2.54033369795628 & -0.000333697956277135 \tabularnewline
50 & 2.66 & 2.54026182300245 & 0.119738176997552 \tabularnewline
51 & 2.66 & 2.68605213960863 & -0.0260521396086304 \tabularnewline
52 & 2.66 & 2.68044078869597 & -0.0204407886959741 \tabularnewline
53 & 2.66 & 2.67603806246973 & -0.0160380624697343 \tabularnewline
54 & 2.66 & 2.67258363616047 & -0.0125836361604659 \tabularnewline
55 & 2.66 & 2.66987325615658 & -0.00987325615658419 \tabularnewline
56 & 2.66 & 2.66774666287951 & -0.00774666287950909 \tabularnewline
57 & 2.66 & 2.66607811494172 & -0.00607811494171973 \tabularnewline
58 & 2.66 & 2.66476895429934 & -0.0047689542993381 \tabularnewline
59 & 2.66 & 2.66374177279095 & -0.00374177279094701 \tabularnewline
60 & 2.66 & 2.66293583514126 & -0.00293583514126272 \tabularnewline
61 & 2.66 & 2.66230348780063 & -0.00230348780062917 \tabularnewline
62 & 2.66 & 2.6618073412819 & -0.00180734128189641 \tabularnewline
63 & 2.66 & 2.66141805939166 & -0.00141805939165618 \tabularnewline
64 & 2.66 & 2.66111262463731 & -0.00111262463730943 \tabularnewline
65 & 2.66 & 2.66087297724681 & -0.000872977246814788 \tabularnewline
66 & 2.66 & 2.66068494732896 & -0.000684947328956742 \tabularnewline
67 & 2.66 & 2.66053741703482 & -0.000537417034815579 \tabularnewline
68 & 2.66 & 2.66042166318066 & -0.000421663180656395 \tabularnewline
69 & 2.66 & 2.66033084146278 & -0.000330841462780285 \tabularnewline
70 & 2.66 & 2.66025958176695 & -0.000259581766954398 \tabularnewline
71 & 2.66 & 2.66020367064385 & -0.000203670643845744 \tabularnewline
72 & 2.66 & 2.66015980217583 & -0.000159802175827561 \tabularnewline
73 & 2.66 & 2.66012538250441 & -0.000125382504405191 \tabularnewline
74 & 2.93 & 2.66009837646033 & 0.26990162353967 \tabularnewline
75 & 2.93 & 2.98823228577943 & -0.0582322857794346 \tabularnewline
76 & 2.93 & 2.97568967719284 & -0.045689677192835 \tabularnewline
77 & 2.93 & 2.96584861171159 & -0.035848611711593 \tabularnewline
78 & 2.93 & 2.95812720598188 & -0.0281272059818818 \tabularnewline
79 & 2.93 & 2.95206890807131 & -0.0220689080713092 \tabularnewline
80 & 2.93 & 2.94731550242757 & -0.0173155024275653 \tabularnewline
81 & 2.93 & 2.94358592927889 & -0.0135859292788849 \tabularnewline
82 & 2.93 & 2.94065966610804 & -0.0106596661080434 \tabularnewline
83 & 2.93 & 2.93836368857827 & -0.0083636885782683 \tabularnewline
84 & 2.93 & 2.93656223993559 & -0.0065622399355898 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157674&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]2.28[/C][C]2.36[/C][C]-0.0799999999999996[/C][/ROW]
[ROW][C]4[/C][C]2.28[/C][C]2.34276885968845[/C][C]-0.0627688596884455[/C][/ROW]
[ROW][C]5[/C][C]2.28[/C][C]2.32924912183235[/C][C]-0.049249121832347[/C][/ROW]
[ROW][C]6[/C][C]2.27[/C][C]2.31864139022592[/C][C]-0.0486413902259217[/C][/ROW]
[ROW][C]7[/C][C]2.28[/C][C]2.29816455747677[/C][C]-0.0181645574767733[/C][/ROW]
[ROW][C]8[/C][C]2.27[/C][C]2.30425210699453[/C][C]-0.0342521069945283[/C][/ROW]
[ROW][C]9[/C][C]2.28[/C][C]2.28687457122466[/C][C]-0.00687457122466517[/C][/ROW]
[ROW][C]10[/C][C]2.28[/C][C]2.29539386245774[/C][C]-0.0153938624577399[/C][/ROW]
[ROW][C]11[/C][C]2.28[/C][C]2.29207818990841[/C][C]-0.0120781899084141[/C][/ROW]
[ROW][C]12[/C][C]2.28[/C][C]2.28947667759565[/C][C]-0.00947667759564563[/C][/ROW]
[ROW][C]13[/C][C]2.27[/C][C]2.28743550307892[/C][C]-0.0174355030789211[/C][/ROW]
[ROW][C]14[/C][C]2.28[/C][C]2.27368008307948[/C][C]0.00631991692052125[/C][/ROW]
[ROW][C]15[/C][C]2.28[/C][C]2.28504132526966[/C][C]-0.00504132526966439[/C][/ROW]
[ROW][C]16[/C][C]2.28[/C][C]2.28395547798119[/C][C]-0.00395547798119233[/C][/ROW]
[ROW][C]17[/C][C]2.27[/C][C]2.28310351053003[/C][C]-0.0131035105300272[/C][/ROW]
[ROW][C]18[/C][C]2.28[/C][C]2.27028115517357[/C][C]0.0097188448264327[/C][/ROW]
[ROW][C]19[/C][C]2.27[/C][C]2.28237448990945[/C][C]-0.012374489909448[/C][/ROW]
[ROW][C]20[/C][C]2.27[/C][C]2.26970915776053[/C][C]0.000290842239472067[/C][/ROW]
[ROW][C]21[/C][C]2.27[/C][C]2.26977180205349[/C][C]0.000228197946511077[/C][/ROW]
[ROW][C]22[/C][C]2.27[/C][C]2.26982095343893[/C][C]0.000179046561072038[/C][/ROW]
[ROW][C]23[/C][C]2.27[/C][C]2.26985951814413[/C][C]0.000140481855870345[/C][/ROW]
[ROW][C]24[/C][C]2.27[/C][C]2.26988977642625[/C][C]0.00011022357374868[/C][/ROW]
[ROW][C]25[/C][C]2.27[/C][C]2.26991351739956[/C][C]8.64826004374208e-05[/C][/ROW]
[ROW][C]26[/C][C]2.35[/C][C]2.26993214482235[/C][C]0.0800678551776546[/C][/ROW]
[ROW][C]27[/C][C]2.54[/C][C]2.36717790040999[/C][C]0.172822099590012[/C][/ROW]
[ROW][C]28[/C][C]2.54[/C][C]2.59440192349715[/C][C]-0.0544019234971493[/C][/ROW]
[ROW][C]29[/C][C]2.54[/C][C]2.58268433378468[/C][C]-0.0426843337846763[/C][/ROW]
[ROW][C]30[/C][C]2.54[/C][C]2.57349058697781[/C][C]-0.0334905869778144[/C][/ROW]
[ROW][C]31[/C][C]2.54[/C][C]2.56627707443618[/C][C]-0.0262770744361762[/C][/ROW]
[ROW][C]32[/C][C]2.54[/C][C]2.56061727497884[/C][C]-0.0206172749788398[/C][/ROW]
[ROW][C]33[/C][C]2.54[/C][C]2.55617653550381[/C][C]-0.0161765355038113[/C][/ROW]
[ROW][C]34[/C][C]2.54[/C][C]2.55269228359105[/C][C]-0.0126922835910488[/C][/ROW]
[ROW][C]35[/C][C]2.54[/C][C]2.54995850209816[/C][C]-0.00995850209815607[/C][/ROW]
[ROW][C]36[/C][C]2.54[/C][C]2.54781354776133[/C][C]-0.00781354776132837[/C][/ROW]
[ROW][C]37[/C][C]2.54[/C][C]2.54613059353875[/C][C]-0.00613059353874723[/C][/ROW]
[ROW][C]38[/C][C]2.54[/C][C]2.54481012957051[/C][C]-0.00481012957050631[/C][/ROW]
[ROW][C]39[/C][C]2.54[/C][C]2.54377407935118[/C][C]-0.00377407935117935[/C][/ROW]
[ROW][C]40[/C][C]2.54[/C][C]2.54296118321559[/C][C]-0.00296118321559069[/C][/ROW]
[ROW][C]41[/C][C]2.54[/C][C]2.54232337617214[/C][C]-0.00232337617213974[/C][/ROW]
[ROW][C]42[/C][C]2.54[/C][C]2.54182294591191[/C][C]-0.00182294591190635[/C][/ROW]
[ROW][C]43[/C][C]2.54[/C][C]2.54143030295205[/C][C]-0.00143030295205104[/C][/ROW]
[ROW][C]44[/C][C]2.54[/C][C]2.54112223106637[/C][C]-0.00112223106636566[/C][/ROW]
[ROW][C]45[/C][C]2.54[/C][C]2.54088051455428[/C][C]-0.000880514554284062[/C][/ROW]
[ROW][C]46[/C][C]2.54[/C][C]2.54069086118139[/C][C]-0.000690861181393831[/C][/ROW]
[ROW][C]47[/C][C]2.54[/C][C]2.54054205710699[/C][C]-0.000542057106988736[/C][/ROW]
[ROW][C]48[/C][C]2.54[/C][C]2.54042530383115[/C][C]-0.000425303831146362[/C][/ROW]
[ROW][C]49[/C][C]2.54[/C][C]2.54033369795628[/C][C]-0.000333697956277135[/C][/ROW]
[ROW][C]50[/C][C]2.66[/C][C]2.54026182300245[/C][C]0.119738176997552[/C][/ROW]
[ROW][C]51[/C][C]2.66[/C][C]2.68605213960863[/C][C]-0.0260521396086304[/C][/ROW]
[ROW][C]52[/C][C]2.66[/C][C]2.68044078869597[/C][C]-0.0204407886959741[/C][/ROW]
[ROW][C]53[/C][C]2.66[/C][C]2.67603806246973[/C][C]-0.0160380624697343[/C][/ROW]
[ROW][C]54[/C][C]2.66[/C][C]2.67258363616047[/C][C]-0.0125836361604659[/C][/ROW]
[ROW][C]55[/C][C]2.66[/C][C]2.66987325615658[/C][C]-0.00987325615658419[/C][/ROW]
[ROW][C]56[/C][C]2.66[/C][C]2.66774666287951[/C][C]-0.00774666287950909[/C][/ROW]
[ROW][C]57[/C][C]2.66[/C][C]2.66607811494172[/C][C]-0.00607811494171973[/C][/ROW]
[ROW][C]58[/C][C]2.66[/C][C]2.66476895429934[/C][C]-0.0047689542993381[/C][/ROW]
[ROW][C]59[/C][C]2.66[/C][C]2.66374177279095[/C][C]-0.00374177279094701[/C][/ROW]
[ROW][C]60[/C][C]2.66[/C][C]2.66293583514126[/C][C]-0.00293583514126272[/C][/ROW]
[ROW][C]61[/C][C]2.66[/C][C]2.66230348780063[/C][C]-0.00230348780062917[/C][/ROW]
[ROW][C]62[/C][C]2.66[/C][C]2.6618073412819[/C][C]-0.00180734128189641[/C][/ROW]
[ROW][C]63[/C][C]2.66[/C][C]2.66141805939166[/C][C]-0.00141805939165618[/C][/ROW]
[ROW][C]64[/C][C]2.66[/C][C]2.66111262463731[/C][C]-0.00111262463730943[/C][/ROW]
[ROW][C]65[/C][C]2.66[/C][C]2.66087297724681[/C][C]-0.000872977246814788[/C][/ROW]
[ROW][C]66[/C][C]2.66[/C][C]2.66068494732896[/C][C]-0.000684947328956742[/C][/ROW]
[ROW][C]67[/C][C]2.66[/C][C]2.66053741703482[/C][C]-0.000537417034815579[/C][/ROW]
[ROW][C]68[/C][C]2.66[/C][C]2.66042166318066[/C][C]-0.000421663180656395[/C][/ROW]
[ROW][C]69[/C][C]2.66[/C][C]2.66033084146278[/C][C]-0.000330841462780285[/C][/ROW]
[ROW][C]70[/C][C]2.66[/C][C]2.66025958176695[/C][C]-0.000259581766954398[/C][/ROW]
[ROW][C]71[/C][C]2.66[/C][C]2.66020367064385[/C][C]-0.000203670643845744[/C][/ROW]
[ROW][C]72[/C][C]2.66[/C][C]2.66015980217583[/C][C]-0.000159802175827561[/C][/ROW]
[ROW][C]73[/C][C]2.66[/C][C]2.66012538250441[/C][C]-0.000125382504405191[/C][/ROW]
[ROW][C]74[/C][C]2.93[/C][C]2.66009837646033[/C][C]0.26990162353967[/C][/ROW]
[ROW][C]75[/C][C]2.93[/C][C]2.98823228577943[/C][C]-0.0582322857794346[/C][/ROW]
[ROW][C]76[/C][C]2.93[/C][C]2.97568967719284[/C][C]-0.045689677192835[/C][/ROW]
[ROW][C]77[/C][C]2.93[/C][C]2.96584861171159[/C][C]-0.035848611711593[/C][/ROW]
[ROW][C]78[/C][C]2.93[/C][C]2.95812720598188[/C][C]-0.0281272059818818[/C][/ROW]
[ROW][C]79[/C][C]2.93[/C][C]2.95206890807131[/C][C]-0.0220689080713092[/C][/ROW]
[ROW][C]80[/C][C]2.93[/C][C]2.94731550242757[/C][C]-0.0173155024275653[/C][/ROW]
[ROW][C]81[/C][C]2.93[/C][C]2.94358592927889[/C][C]-0.0135859292788849[/C][/ROW]
[ROW][C]82[/C][C]2.93[/C][C]2.94065966610804[/C][C]-0.0106596661080434[/C][/ROW]
[ROW][C]83[/C][C]2.93[/C][C]2.93836368857827[/C][C]-0.0083636885782683[/C][/ROW]
[ROW][C]84[/C][C]2.93[/C][C]2.93656223993559[/C][C]-0.0065622399355898[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157674&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157674&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
t	Observed	Fitted	Residuals
3	2.28	2.36	-0.0799999999999996
4	2.28	2.34276885968845	-0.0627688596884455
5	2.28	2.32924912183235	-0.049249121832347
6	2.27	2.31864139022592	-0.0486413902259217
7	2.28	2.29816455747677	-0.0181645574767733
8	2.27	2.30425210699453	-0.0342521069945283
9	2.28	2.28687457122466	-0.00687457122466517
10	2.28	2.29539386245774	-0.0153938624577399
11	2.28	2.29207818990841	-0.0120781899084141
12	2.28	2.28947667759565	-0.00947667759564563
13	2.27	2.28743550307892	-0.0174355030789211
14	2.28	2.27368008307948	0.00631991692052125
15	2.28	2.28504132526966	-0.00504132526966439
16	2.28	2.28395547798119	-0.00395547798119233
17	2.27	2.28310351053003	-0.0131035105300272
18	2.28	2.27028115517357	0.0097188448264327
19	2.27	2.28237448990945	-0.012374489909448
20	2.27	2.26970915776053	0.000290842239472067
21	2.27	2.26977180205349	0.000228197946511077
22	2.27	2.26982095343893	0.000179046561072038
23	2.27	2.26985951814413	0.000140481855870345
24	2.27	2.26988977642625	0.00011022357374868
25	2.27	2.26991351739956	8.64826004374208e-05
26	2.35	2.26993214482235	0.0800678551776546
27	2.54	2.36717790040999	0.172822099590012
28	2.54	2.59440192349715	-0.0544019234971493
29	2.54	2.58268433378468	-0.0426843337846763
30	2.54	2.57349058697781	-0.0334905869778144
31	2.54	2.56627707443618	-0.0262770744361762
32	2.54	2.56061727497884	-0.0206172749788398
33	2.54	2.55617653550381	-0.0161765355038113
34	2.54	2.55269228359105	-0.0126922835910488
35	2.54	2.54995850209816	-0.00995850209815607
36	2.54	2.54781354776133	-0.00781354776132837
37	2.54	2.54613059353875	-0.00613059353874723
38	2.54	2.54481012957051	-0.00481012957050631
39	2.54	2.54377407935118	-0.00377407935117935
40	2.54	2.54296118321559	-0.00296118321559069
41	2.54	2.54232337617214	-0.00232337617213974
42	2.54	2.54182294591191	-0.00182294591190635
43	2.54	2.54143030295205	-0.00143030295205104
44	2.54	2.54112223106637	-0.00112223106636566
45	2.54	2.54088051455428	-0.000880514554284062
46	2.54	2.54069086118139	-0.000690861181393831
47	2.54	2.54054205710699	-0.000542057106988736
48	2.54	2.54042530383115	-0.000425303831146362
49	2.54	2.54033369795628	-0.000333697956277135
50	2.66	2.54026182300245	0.119738176997552
51	2.66	2.68605213960863	-0.0260521396086304
52	2.66	2.68044078869597	-0.0204407886959741
53	2.66	2.67603806246973	-0.0160380624697343
54	2.66	2.67258363616047	-0.0125836361604659
55	2.66	2.66987325615658	-0.00987325615658419
56	2.66	2.66774666287951	-0.00774666287950909
57	2.66	2.66607811494172	-0.00607811494171973
58	2.66	2.66476895429934	-0.0047689542993381
59	2.66	2.66374177279095	-0.00374177279094701
60	2.66	2.66293583514126	-0.00293583514126272
61	2.66	2.66230348780063	-0.00230348780062917
62	2.66	2.6618073412819	-0.00180734128189641
63	2.66	2.66141805939166	-0.00141805939165618
64	2.66	2.66111262463731	-0.00111262463730943
65	2.66	2.66087297724681	-0.000872977246814788
66	2.66	2.66068494732896	-0.000684947328956742
67	2.66	2.66053741703482	-0.000537417034815579
68	2.66	2.66042166318066	-0.000421663180656395
69	2.66	2.66033084146278	-0.000330841462780285
70	2.66	2.66025958176695	-0.000259581766954398
71	2.66	2.66020367064385	-0.000203670643845744
72	2.66	2.66015980217583	-0.000159802175827561
73	2.66	2.66012538250441	-0.000125382504405191
74	2.93	2.66009837646033	0.26990162353967
75	2.93	2.98823228577943	-0.0582322857794346
76	2.93	2.97568967719284	-0.045689677192835
77	2.93	2.96584861171159	-0.035848611711593
78	2.93	2.95812720598188	-0.0281272059818818
79	2.93	2.95206890807131	-0.0220689080713092
80	2.93	2.94731550242757	-0.0173155024275653
81	2.93	2.94358592927889	-0.0135859292788849
82	2.93	2.94065966610804	-0.0106596661080434
83	2.93	2.93836368857827	-0.0083636885782683
84	2.93	2.93656223993559	-0.0065622399355898

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	2.93514880397199	2.84853983713336	3.02175777081062
86	2.94029760794397	2.80398348461483	3.07661173127312
87	2.94544641191596	2.76122569514044	3.12966712869148
88	2.95059521588795	2.71764822365452	3.18354220812138
89	2.95574401985993	2.67244450068313	3.23904353903674
90	2.96089282383192	2.6253094320233	3.29647621564055
91	2.96604162780391	2.57612743428259	3.35595582132523
92	2.97119043177589	2.52486632850173	3.41751453505006
93	2.97633923574788	2.47153374383743	3.48114472765834
94	2.98148803971987	2.41615697914503	3.5468191002947
95	2.98663684369185	2.35877295193705	3.61450073544666
96	2.99178564766384	2.2994229165306	3.68414837879709

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 2.93514880397199 & 2.84853983713336 & 3.02175777081062 \tabularnewline
86 & 2.94029760794397 & 2.80398348461483 & 3.07661173127312 \tabularnewline
87 & 2.94544641191596 & 2.76122569514044 & 3.12966712869148 \tabularnewline
88 & 2.95059521588795 & 2.71764822365452 & 3.18354220812138 \tabularnewline
89 & 2.95574401985993 & 2.67244450068313 & 3.23904353903674 \tabularnewline
90 & 2.96089282383192 & 2.6253094320233 & 3.29647621564055 \tabularnewline
91 & 2.96604162780391 & 2.57612743428259 & 3.35595582132523 \tabularnewline
92 & 2.97119043177589 & 2.52486632850173 & 3.41751453505006 \tabularnewline
93 & 2.97633923574788 & 2.47153374383743 & 3.48114472765834 \tabularnewline
94 & 2.98148803971987 & 2.41615697914503 & 3.5468191002947 \tabularnewline
95 & 2.98663684369185 & 2.35877295193705 & 3.61450073544666 \tabularnewline
96 & 2.99178564766384 & 2.2994229165306 & 3.68414837879709 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157674&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]2.93514880397199[/C][C]2.84853983713336[/C][C]3.02175777081062[/C][/ROW]
[ROW][C]86[/C][C]2.94029760794397[/C][C]2.80398348461483[/C][C]3.07661173127312[/C][/ROW]
[ROW][C]87[/C][C]2.94544641191596[/C][C]2.76122569514044[/C][C]3.12966712869148[/C][/ROW]
[ROW][C]88[/C][C]2.95059521588795[/C][C]2.71764822365452[/C][C]3.18354220812138[/C][/ROW]
[ROW][C]89[/C][C]2.95574401985993[/C][C]2.67244450068313[/C][C]3.23904353903674[/C][/ROW]
[ROW][C]90[/C][C]2.96089282383192[/C][C]2.6253094320233[/C][C]3.29647621564055[/C][/ROW]
[ROW][C]91[/C][C]2.96604162780391[/C][C]2.57612743428259[/C][C]3.35595582132523[/C][/ROW]
[ROW][C]92[/C][C]2.97119043177589[/C][C]2.52486632850173[/C][C]3.41751453505006[/C][/ROW]
[ROW][C]93[/C][C]2.97633923574788[/C][C]2.47153374383743[/C][C]3.48114472765834[/C][/ROW]
[ROW][C]94[/C][C]2.98148803971987[/C][C]2.41615697914503[/C][C]3.5468191002947[/C][/ROW]
[ROW][C]95[/C][C]2.98663684369185[/C][C]2.35877295193705[/C][C]3.61450073544666[/C][/ROW]
[ROW][C]96[/C][C]2.99178564766384[/C][C]2.2994229165306[/C][C]3.68414837879709[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157674&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157674&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
t	Forecast	95% Lower Bound	95% Upper Bound
85	2.93514880397199	2.84853983713336	3.02175777081062
86	2.94029760794397	2.80398348461483	3.07661173127312
87	2.94544641191596	2.76122569514044	3.12966712869148
88	2.95059521588795	2.71764822365452	3.18354220812138
89	2.95574401985993	2.67244450068313	3.23904353903674
90	2.96089282383192	2.6253094320233	3.29647621564055
91	2.96604162780391	2.57612743428259	3.35595582132523
92	2.97119043177589	2.52486632850173	3.41751453505006
93	2.97633923574788	2.47153374383743	3.48114472765834
94	2.98148803971987	2.41615697914503	3.5468191002947
95	2.98663684369185	2.35877295193705	3.61450073544666
96	2.99178564766384	2.2994229165306	3.68414837879709

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code